Rakesh Halder <[email protected]> writes: > Hi all, > > I'm wondering what the recommended method is to solve linear systems Ax=b, > where A is an N by n matrix (N >> n) and dense. I've used the CGLS and LSQR > algorithms, but have issues applying any kind of preconditioner. Looking at > the PETSc documentation, it doesn't look like there are any direct solvers > for rectangular systems, but only iterative ones which aren't very useful > for dense systems.
QR is the standard technique. For a highly parallel implementation, I would check out BVOrthogonalize() from SLEPc, which has several good options. Arguably, this feature should be migrated to PETSc. > I'm also wondering if it's best to use a dense or sparse (AIJ) matrix > format in general when working with dense matrices. I've just been using > sparse matrices, due to being able to preallocate memory. > > Thanks, > > Rakesh Halder
